MUMBAI — At least 112 people died Saturday and Sunday in a fire at a garment factory outside Dhaka, Bangladesh, in one of the worst industrial tragedies in that country.

It took firefighters all night to put out the blaze at the factory, Tazreen Fashions, after it started Saturday about 7 p.m. local time, according to Salim Nawaj Bhuiyan, a retired fire official who spoke by telephone from Dhaka, the capital.

Scores of workers were taken to hospitals with burns and smoke inhalation injuries. Officials

said that many of the survivors were critically hurt and that the death toll might climb.

Bhuiyan, who runs a fire safety company in Dhaka, said firefighters did not have an adequate approach road to bring their equipment to the site. Fire officials said many of the workers were trapped in the building because it had too few emergency exits.

Major Mohammad Mahbub, operations director for the fire department, said the blaze may have been caused by an electrical fault or by a spark from a cigarette, the Associated Press reported.

The garment industry in Bangladesh, the world’s second-largest exporter of clothing after China, has a notoriously poor record of fire safety. Since 2006, more than 500 Bangladeshi workers have died in garment factory fires, according to Clean Clothes Campaign, an ­antisweatshop advocacy group based in Amsterdam.

Analysts say many of the fires could have been easily avoided if the factories had taken precautions. Many factories are in cramped neighborhoods, have too few fire escapes, and widely flout safety measures. The industry employs more than 3 million workers in Bangladesh, mostly women.

Activists say that global clothing brands like Walmart, Tommy Hilfiger, and the Gap need to take responsibility for working conditions in Bangladeshi factories that produce the clothes they sell.

‘‘These brands have known for years that many of the factories they choose to work with are death traps,’’ said Ineke Zeldenrust, the international coordinator for Clean Clothes Campaign. ‘‘Their failure to take action amounts to criminal negligence.’’

The fire at the Tazreen factory in Savar, northwest of Dhaka, started in a warehouse on the ground floor used to store yarn, according to a garment industry official at the scene who asked not to be named because he was not authorized to speak to the media.

It quickly spread up the building, which was nine stories high, with the top three floors under construction. Though most workers had left for the day when the fire started, the industry official said as many as 600 workers were still inside, working overtime.

POLASH KHAN/ASSOCIATED PRESS

Bangladeshis identified bodies of relatives who died in the garment factory fire.

The factory, which started operations in May 2010, employed about 1,500 workers and had sales of $35 million a year, according to a document on the company’s website. It made T-shirts, polo shirts, and fleece jackets.

Most of the workers who died were on the first and second floors and were killed, fire officials said, because there were not enough exits for them to get out and none that opened to the outside. Mahbub said the factory had three interior staircases to the ground floor.

In a brief phone call, Delowar Hossain, the managing director of the Tuba Group, the parent company of Tarzeen Fashions, said he was too busy to comment. ‘‘Pray for me,’’ he said and then hung up.

Television news reports showed badly burned bodies lined up on the floor in what appeared to be a government building and showed the injured receiving treatment in hallways of local hospitals.

The industry official said many bodies were burned beyond recognition and it would take time to identify them.

One survivor, Mohammad Raju, 22, who worked on the fifth floor, said he escaped by climbing out of a third-floor window onto the bamboo scaffolding that was being used by construction workers. But he said he lost his mother, who also worked on the fifth floor, when they were making their way down.

‘‘It was crowded on the stairs as all the workers were trying to come out from the factory,’’ Raju said. ‘‘There was no power supply, it was dark, and I lost my mother in the dark. I tried to search for her for 10 to 15 minutes but did not find her.’’

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